Finding the Embedding Dimension and Variable Dependencies in Time Series

Pi, Hong; Peterson, Carsten

doi:10.1162/neco.1994.6.3.509

Cited by 126 publications

(78 citation statements)

References 5 publications

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“…Delta Test (DT), introduced for time series in 1994 [41], is a NNE method, i.e., it estimates the lowest mean square error (MSE) that can be achieved by a model without overfitting the training set [24]. Given N multiple input-single output pairs, (x i , y i ) ∈ R M × R, the theory behind the DT method considers that the mapping betweenx i and y i is given by the following expression:…”

Section: Nonparametric Residual Variance Estimation: Delta Testmentioning

confidence: 99%

Autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation

Pouzols¹,

Lendasse²,

Barriga³

2010

Fuzzy Sets and Systems

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We propose an automatic methodology framework for short-and long-term prediction of time series by means of fuzzy inference systems. In this methodology, fuzzy techniques and statistical techniques for nonparametric residual variance estimation are combined in order to build autoregressive predictive models implemented as fuzzy inference systems. Furthermore, fuzzy models are shown to be consistently more accurate for prediction in the case of time series coming from real-world applications

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Section: Nonparametric Residual Variance Estimation: Delta Testmentioning

confidence: 99%

Autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation

Pouzols¹,

Lendasse²,

Barriga³

2010

Fuzzy Sets and Systems

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“…Delta Test was introduced by Pi and Peterson for time series [42] and recently further analyzed by Liitiäinen et al [43]. However, its applicability to variable selection was proposed in [35].…”

Section: Delta Testmentioning

confidence: 99%

Approximate k-NN delta test minimization method using genetic algorithms: Application to time series

2010

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In many real world problems, the existence of irrelevant input variables (features) hinders the predictive quality of the models used to estimate the output variables. In particular, time series prediction often involves building large regressors of artificial variables that can contain irrelevant or misleading information. Many techniques have arisen to confront the problem of accurate variable selection, including both local and global search strategies. This paper presents a method based on genetic algorithms that intends to find a global optimum set of input variables that minimize the Delta Test criterion. The execution speed has been enhanced by substituting the exact nearest neighbor computation by its approximate version. The problems of scaling and projection of variables have been addressed. The developed method works in conjunction with MATLAB's Genetic Algorithm and Direct Search Toolbox. The goodness of the proposed methodology has been evaluated on several popular time series examples, and also generalized to other non-time-series datasets.

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“…The DT, firstly introduced by Pi and Peterson for time series [2] and proposed for variable selection in [10], is a technique to estimate the variance of the noise, or the mean squared error (MSE), that can be achieved without overfitting. Given N input-output pairs (x i , y i ) ∈ R d × R, the relationship between x i and y i can be expressed as…”

Section: The Delta Testmentioning

confidence: 99%

“…One of the most successful criteria to determine the optimal set of variables in regression applications is a nonparametric noise estimator called Delta Test (DT) ( [2], [3]). …”

Section: Introductionmentioning

confidence: 99%

RCGA-S/RCGA-SP Methods to Minimize the Delta Test for Regression Tasks

Mateo

Sovilj

Gadea

et al. 2009

Lecture Notes in Computer Science

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Abstract. Frequently, the number of input variables (features) involved in a problem becomes too large to be easily handled by conventional machine-learning models. This paper introduces a combined strategy that uses a real-coded genetic algorithm to find the optimal scaling (RCGA-S) or scaling + projection (RCGA-SP) factors that minimize the Delta Test criterion for variable selection when being applied to the input variables. These two methods are evaluated on five different regression datasets and their results are compared. The results confirm the goodness of both methods although RCGA-SP performs clearly better than RCGA-S because it adds the possibility of projecting the input variables onto a lower dimensional space.

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Finding the Embedding Dimension and Variable Dependencies in Time Series

Cited by 126 publications

References 5 publications

Autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation

Autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation

Approximate k-NN delta test minimization method using genetic algorithms: Application to time series

RCGA-S/RCGA-SP Methods to Minimize the Delta Test for Regression Tasks

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